Hawkes processes: stochastic control and cyber-security

Hawkes processes are widely used in many applications, thanks to their self-exciting behavior. In this thesis, we study these processes and their properties in order to formalize stochastic optimization problems where the system dynamics are driven by Hawkes-diffusion processes. We apply our results to a cyber-security investment model, whose goal is to determine the optimal strategy to mitigate the impact of cyberattacks. The proposed model is a dynamic and stochastic extension of the static and deterministic Gordon Loeb model.